Show that 23377 is a Fermat pseudoprime base b 2 What does

Show that 23377 is a Fermat pseudoprime base b = 2. What does the Miller-Rabin test say about 23377 with base b = 2?

Solution

solution:we know that a composite number n is Fermat Psedoprime to base b if b^n-1= 1(mod n).

here given that n=23377 and base =2.

so 2²³³⁷⁶ =1( mod 23377) mens that when we divide 2²³³⁷⁶ by 23377 we got remander is 1.so 23377 is a fermat pseudoprime with base 2.

Now Miller Rabin test for the number 23377 with base 2.

the miller rabin primality test say if we can find base b such that b^d not equavalent to1(mod n) and b^2r.d is not equvalent to -1(mod n).where 0<= r <= s-1.and s,d are posative and d is odd.

here n=23377 and base=2.

so 2²³³⁷⁶=1(mod 23377) therefore by miller-rabin test is not peime .